Officially, the app resides on Apple's servers, bought through the App Store, and then downloaded to your devices.
There is a way, usually for development builds of applications, to tell the app which devices specifically to run on (like for business use, not for the general public), which then you can take the application file, import it into iTunes, then sync to devices.
But in order for that to work, the application must know the device ID to allow its import. You can't just download a random file and expect it to work.
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